Digital to analog converters (DAC) are used to convert a digital representation of a signal into an analog representation of the same signal. DACs are used in a wide variety of applications, ranging from medical and entertainment to communications (both voice and data). Digital to analog converters are electrical circuit devices that convert a digital signal that is a series of multi-bit samples, or numbers, in the digital domain to a continuous signal, such as a voltage or current, in the analog domain. A variety of DAC converter types exist, including a thermometer DAC, R-2R ladder network DAC, segmented DAC, oversampling/interpolating DAC, and pulse-width modulated DAC, for example. Another type is known as a sigma delta or delta sigma (ΔΣ) D/A converter. It consists of an “interpolation filter” that is a digital circuit which accepts data at a low rate, inserts zeros at a high rate, and then applies a digital filter algorithm and outputs data at a high rate, a ΣΔ modulator that effectively acts as a low pass filter to the signal but as a high pass filter to the quantization noise, and converts the resulting data to a high speed bit stream, and a 1-bit DAC whose output switches between equal positive and negative reference voltages. The output is filtered in an external analog low pass filter (LPF). It is also possible to use more than one bit in the ΣΔ DAC. The general operation of the various types of DACs are well known and described in the literature, for example “The Data Conversion Handbook,” James Bryant, Walt Kester (2005), Chapter 3, which is incorporated by reference herein.
The oversampling in a sigma delta DAC is commonly performed at a multiple of the Nyquist rate (FN) for a given input signal frequency and typically the sampling frequency FS is 10 to 1000 times FN. In this manner, quantization noise power is spread over a bandwidth equal to the sampling frequency, thereby reducing the noise density in the band of interest. Sigma-delta DACs are commonly used in applications where high resolution with low to moderate conversion rates are required. An advantage of sigma-delta DACs is that the sigma-delta DACs normally make use of single or low multi-bit (typically two, three, four or six bit) quantizer, making the precision requirements of the sigma-delta DAC much lower than other types of DACs that may use quantizers with a large number of bits. However, sigma-delta DACs having a larger number of elements, such as 32 or 64 elements, are now becoming more common. Operating at a frequency greater than the required frequency is commonly referred to as oversampling and a DAC that is operating at a frequency that is K times greater than the required frequency is referred to as a K-times oversampling DAC.
Non-linearity may be a problem when using a sigma delta signal converter. There are two major sources of non-linearity: static and dynamic. FIG. 1 is a block diagram of a prior art digital to analog converter 100 illustrating an upsampling module, a sigma delta module (SDM), static mismatch shaping module 102 and six unit weight DAC segments 104, whose summed output is then fed through a low pass filter module. Mismatch shaping modules are typically referred to as Dynamic Element Matching (DEM) or Data Weighted Average (DEM) modules.
FIG. 2 is a more detailed block diagram of prior art mismatch shaping module 102 that is used in the signal converter of FIG. 1. The SDM updates every sample with the number of segments to use N(k) in the range 0 . . . M. Mismatch shaper 102 is a vectorized sigma-delta loop that includes a vector quantizer 208 and M loop filters 206. The loop filters integrate the usage history of each of the M segments. The vector quantizer looks at the loop filter output plus dither signal vector e(k) and picks the N vector indices with highest values. The output segment control vector s(k) is formed so that si(k)=1 for all the picked indices i and zero otherwise.
Each segment 104 is thus controlled by its own 1-bit sigma-delta modulator that will replicate the SDM signal plus a high-pass shaped quantization error. The high-pass shaping reduces the sensitivity to element mismatch which causes non-uniform weighting. The vector quantizer needs to implement a sorting of M elements and there are numerous sorting algorithms. The simpler algorithms have O(M2) complexity which will give gate counts that scale with M2. The theoretically best algorithms have O(MlogM) complexity.
All M elements need to be used by the same frequency on average—this eliminates the DC error due to mismatches. Moreover, the mismatch shaper should force each element to toggle in patterns that concentrates the AC mismatch error at high frequencies and reduces the audio band errors
Mismatch shaping does not address dynamic errors, however. Several schemes for addressing dynamic errors have been used. For example, the DEM may be operated at half the clock rate, as described in Ido et al, U.S. Pat. No. 7,215,271 B2. In this case, the number of transitions will be restricted and dynamic error power is reduced to 4.6·Δ2→ better than R2DWA. However, this scheme compromises the static mismatch algorithm and Noise due to static mismatch will increase.
In another solution the sampling clock frequency is cut by half, which reduces the dynamic error by 6 dB. However, out-of band noise moves into the band and therefore requires the order of the SDM be increased to compensate. Higher order modulators are more unstable and have limited stable input range.
Another solution is to limit the operation of the vector quantizer, as described by R. Schreier, Mismatch Shaping for a Current-Mode Multibit Delta-Sigma DAC, IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 34, NO. 3, MARCH 1999. The vector quantizer makes decisions such that switching rate can get only restricted values. For example, for 8-level DAC only 3,4,5 elements can switch at a time. This method also compromises static mismatch shaping.
Mobile audio devices are a ubiquitous fixture of modern society. Cellular telephones, personal music players, portable gaming systems, etc. are constant companions for many people. Music players and gaming systems may make use of ΣΔ DACs to produce the audio signal(s) that are then reproduced by a speaker. Cell phones continue to increase in computer processing capability and sophistication. The basic radio transceiver within the cell phone may make use of a sigma-delta DAC for signal modulation and transmission. The increased memory capacity and computing resources on a cell phone support the installation of various applications, often referred to as “apps” that allow a diverse range of functions to be performed by the cell phone when not being used for conversation. Digital to analog conversion of audio signals to drive speakers/headsets is required by several apps that run on a mobile device and may be performed by a sigma-delta DAC.